They might even go further, and when you tell the car to take you to the supermarket, it'll take you to whichever one paid the automaker for preferential treatment, even if it's a lot further away than the nearest supermarket.

This is why open firmware is really important. There have even been ethical arguements like how do you know that the government won't back door it and then lock you in and crash it into a wall or some shit. Or in a much more likely, someone with a similar name has a warrant out for their arrest, someone messes up and when you get in your car, it locks you in and drives you to the police station.